A multiformalism and multiresolution modelling environment: application to the cardiovascular system and its regulation

The role of modelling and simulation in the systemic analysis of living systems is now clearly established. Emerging disciplines, such as systems biology, and worldwide research actions, such as the Physiome Project or the Virtual Physiological Human, are based on an intensive use of modelling and simulation methodologies and tools. One of the key aspects in this context is to perform an efficient integration of various models representing different biological or physiological functions, at different resolutions, spanning through different scales. This paper presents a multiformalism modelling and simulation environment (M2SL) that has been conceived to ease model integration. A given model is represented as a set of coupled and atomic model components that may be based on different mathematical formalisms with heterogeneous structural and dynamical properties. A co-simulation approach is used to solve these hybrid systems. The pioneering model of the overall regulation of the cardiovascular system proposed by Guyton and co-workers in 1972 has been implemented under M2SL and a pulsatile ventricular model based on a time-varying elastance has been integrated in a multi-resolution approach. Simulations reproducing physiological conditions and using different coupling methods show the benefits of the proposed environment.